Marinada '22

[lang=hr] Sada jedino tražimo da $f$ bude prirodan broj veći od 1, ostali mogu biti bilokoji prirodni brojevi. Trojka je nenaspavana ako zadovoljava jednadžbu $$3^c=i^f+1$$ Odredite umnožak umora svih nenaspavanih trojki [/lang] [lang=en] This time the only condition is that $f$ be positive integer greater than $1$, $c$ and $i$ may be any positive integers. Triple $(c,i,f)$ is said to be sleepless if it satisfies $$3^c=i^f+1$$ Determine the product of tiredness' of all sleepless triples. [/lang]